Originally Posted by NateTheGreat
The Shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1to8 ratios?

Hi NateTheGreat! Welcome to PF!
You've left out that at noon during the summer solstice, the sun at Syene is
directly overhead.
(I know that 'cos this is a wellknown experiment by Eratosthenes in about 200 BC )
Does that help?